MAT 153 College Algebra and Trigonometry

This is a sample syllabus only. Ask your instructor for the official syllabus for your course.

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Course Description

Functions, including their graphs, domain, range, inverse functions. Standard algebraic transformations of functions and the corresponding geometric transformations of their graphs. Exponential and logarithmic functions and equations; exponential growth and decay. Right-triangle trigonometry and applications. Trigonometric and inverse trigonometric functions and their graphs. Harmonic motion and sinusoids. Trigonometric identities and equations. The laws of sines and cosines.

MAT 153 meets for four hours of lecture per week.

Prerequisites

MAT 009 or equivalent.

Objectives

After completing MAT 153 the student should be able to

• obtain the domain and graph of linear, quadratic, exponential, logarithmic, trigonometric, and inverse trigonometric functions
• understand the Vertical and Horizontal Line Tests
• find the composition of two functions algebraically, and the inverse of a function, both algebraically and geometrically
• understand the effects on the graph of a function (e.g. translations and/or reflections) due to standard algebraic changes to the function
• use laws of exponents and logarithms and trigonometric identities
• simplify expressions involving exponential, logarithmic, and trigonometric functions
• solve exponential, logarithmic, and trigonometric equations
• prove trigonometric identities
• solve standard exponential growth and decay problems
• understand the correspondence between the symmetries of the trigonometric circle and the symmetries of the trigonometric functions
• use a graphic calculator to graph and evaluate exponential, logarithmic, and trigonometric functions
• solve triangles using the Laws of Sines and Cosines
• apply trigonometry to surveying, navigation, area, and angular speed problems and harmonic oscillations
• throughout, use standard mathematical notation and terminology and avoid nonsensical expressions and statements.

Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 153.

Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of topics covered in MAT 153.

Text

Precalculus (5th ed.), by David Cohen. West Publ., 1997.

Course Coverage

MAT 153 covers the following sections in the text.

• Chapter 3 Functions
• • 3.1 The Definition of a Function
  • 3.2 The Graph of a Function
  • 3.3 Techniques in Graphing
  • 3.4 Method of Combining Functions. Iteration ("Iteration" , if time allows)
  • 3.5 Inverse Functions
• Chapter 5 Exponential and Logarithmic Functions
• • 5.1 Exponential Functions
  • 5.2 The Natural Exponential Function
  • 5.3 Logarithmic Functions
  • 5.4 Properties of Logarithms
  • 5.5 Equations and Inequalities with Logs and Exponents
  • 5.6 Compound Interest (if time allows)
  • 5.7 Exponential Growth and Decay
• Chapter 6 Trigonometric Functions of Angles
• • 6.1 Trigonometric Functions of Acute Angles
  • 6.2 Algebra and Trigonometric Functions
  • 6.3 Right-Triangle Applications
  • 6.4 Trigonometric Functions of Angles
  • 6.5 Trigonometric Identities
• Chapter 7 Trigonometric Functions of Real Numbers
• • 7.1 Radian Measure
  • 7.2 Radian Measure and Geometry
  • 7.3 Trigonometric Functions of Real Numbers
  • 7.4 Graphs of the Sine and the Cosine Functions
  • 7.5 Graphs of Sinusoids
  • 7.6 Simple Harmonic Motion
  • 7.7 Graphs of the Tangent and the Reciprocal Functions
• Chapter 8 Analytic Trigonometric
• • 8.1 The Addition Formulas
  • 8.2 The Double-Angle Formulas
  • 8.3 The Product-to-Sum and Sum-to-Product Formulas
  • 8.4 Trigonometric Equations
  • 8.5 The Inverse Trigonometric Functions
• Chapter 9 Additional Topics in Trigonometry
• • 9.1 The Law of Sines and the Law of Cosines
• Chapter 11 Analytic Geometry (if time allows)
• • 11.2 The Parabola
  • 11.4 The Ellipse
  • 11.5 The Hyperbola

Grading Policy

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 153. The instructor determines the relative weights of these factors. Instructore are encouraged to allow the use of graphing calculators on tests and homework. Students may be allowed to use sheet of formulas (written by the student or provided by the instructor) during tests at the instructor's discretion.

Attendance Requirements

Attendance policy is set by the instructor.

Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.

Academic Integrity

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.

Revision history:

Prepared by F. Brulois. Revised 1/2/01 (F. Brulois), 7/6/01, 7/25/06 (G. Jennings).